Dimensional Analysis

Before I came to college, I had never heard of dimensional analysis.  Once I learned what it was, I realized that it was just another example of scientists giving simple things scary names.  Dimensional analysis is extremely useful when you don't know an equation, but know the units.

The first dimensional analysis problem asked me to find the relationship between pressure, density, and the speed of sound in a gas. I knew that the speed of sound had units of m/s and density had units of g/cm^3.  I had always heard of pressure in units of lbs/in^2, and it took me a few minutes of thought to recognize that that translated into science units of N/m^2.  (To get to this point, I first had to remember that pounds were actually a unit of force achieved by multiplying mass and the gravity at earth's surface.)  With this knowledge, I was able to rearrange the units of pressure and density to become m/s in the following way:

Cs^2 = gm/(m^2 s^2 ) * m^3/g

         = g/(ms^2 ) * m^3/g

         = m^2/s^2 

Cs = √(m^2/s^2 )

     = √(P/ρ)